Problem: There is a light source on the plane. This source is so small that it can be represented as point. The light source is moving from point (a, s_y) to the (b, s_y) (s_y < 0) with speed equal to 1 unit per second. The trajectory of this light source is a straight segment connecting these two points. 

There is also a fence on OX axis represented as n segments (l_i, r_i) (so the actual coordinates of endpoints of each segment are (l_i, 0) and (r_i, 0)). The point (x, y) is in the shade if segment connecting (x,y) and the current position of the light source intersects or touches with any segment of the fence.

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You are given q points. For each point calculate total time of this point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y).

Input

First line contains three space separated integers s_y, a and b (-10^9 ≤ s_y < 0, 1 ≤ a < b ≤ 10^9) — corresponding coordinates of the light source.

Second line contains single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — number of segments in the fence.

Next n lines contain two integers per line: l_i and r_i (1 ≤ l_i < r_i ≤ 10^9, r_{i - 1} < l_i) — segments in the fence in increasing order. Segments don't intersect or touch each other.

Next line contains single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — number of points to check.

Next q lines contain two integers per line: x_i and y_i (1 ≤ x_i, y_i ≤ 10^9) — points to process.

Output

Print q lines. The i-th line should contain one real number — total time of the i-th point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y). The answer is considered as correct if its absolute of relative error doesn't exceed 10^{-6}.

Example

Input

-3 1 6
2
2 4
6 7
5
3 1
1 3
6 1
6 4
7 6


Output

5.000000000000000
3.000000000000000
0.000000000000000
1.500000000000000
2.000000000000000

Note

  * The 1-st point is always in the shade; 
  * the 2-nd point is in the shade while light source is moving from (3, -3) to (6, -3); 
  * the 3-rd point is in the shade while light source is at point (6, -3). 
  * the 4-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and at point (6, -3); 
  * the 5-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and from (5.5, -3) to (6, -3); 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
double sy, a, b;
double fencel[200005];
double fencer[200005];
double pre[200005];
int main() {
  scanf("%lf%lf%lf", &sy, &a, &b);
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%lf%lf", &fencel[i], &fencer[i]);
    pre[i + 1] = pre[i] + (fencer[i] - fencel[i]);
  }
  int q;
  scanf("%d", &q);
  for (int i = 0; i < q; i++) {
    double x, y;
    scanf("%lf%lf", &x, &y);
    double sfb = (y - 0) / (y - sy);
    double pax = a - x;
    double pbx = b - x;
    pax = pax * sfb;
    pbx = pbx * sfb;
    pax = x + pax;
    pbx = x + pbx;
    if (pbx <= fencel[0]) {
      printf("0.000000000000000\n");
      continue;
    }
    if (pax >= fencer[n - 1]) {
      printf("0.000000000000000\n");
      continue;
    }
    int l = 0, r = n - 1, mid;
    while (l <= r) {
      mid = (l + r) / 2;
      if (fencer[mid] > pax + 1e-8)
        r = mid - 1;
      else
        l = mid + 1;
    }
    l = r + 1;
    double left = pre[l + 1];
    left -= min(fencer[l] - fencel[l], (fencer[l] - pax));
    l = 0, r = n - 1;
    while (l <= r) {
      mid = (l + r) / 2;
      if (fencel[mid] < pbx - 1e-8)
        l = mid + 1;
      else
        r = mid - 1;
    }
    r = l - 1;
    double right = pre[n] - pre[r];
    right -= min(fencer[r] - fencel[r], pbx - fencel[r]);
    double time = (b - a) * (pre[n] - right - left) / (pbx - pax);
    printf("%.15f\n", time);
  }
  return 0;
}